Class 7 Maths Chapter 1 Solutions

Get Class 7 Maths Chapter 1 solutions and easy explanations for Large Numbers Around Us. Learn lakhs, crores, millions, number systems, estimation, rounding and number patterns with step-by-step examples and original practice questions.

Table of Contents

Class 7 Maths Chapter 1, Large Numbers Around Us, introduces students to numbers much larger than the quantities they normally use in everyday calculations. The chapter develops an understanding of lakhs and crores along with the million and billion system used internationally.

The current NCERT Mathematics textbook for Grade 7 is Ganita Prakash, Part I. NCERT’s official 2026–27 reprint identifies Large Numbers Around Us as Chapter 1 and describes the chapter as an introduction to lakhs, crores, millions and billions through practical situations and exploration.

This chapter is not only about reading large numbers. It also develops skills such as:

understanding place value;
reading and writing large numbers;
comparing quantities;
using the Indian and International number systems;
distinguishing exact and approximate values;
rounding numbers;
estimating calculations;
identifying useful patterns in products.

The aim of this page is to explain these ideas in simple language so that a Class 7 student can understand the method instead of simply memorising answers.

Class 7 Maths Chapter 1 Overview

Particular	Details
Class	7
Subject	Mathematics
Book	Ganita Prakash, Part I
Chapter	1
Chapter Name	Large Numbers Around Us
Main Topic	Large numbers and their applications
Academic reference	2026–27
Level	Class 7

The official NCERT textbook is a 2026–27 reprint of the Grade 7 Ganita Prakash Part I textbook.

What Does “Large Numbers Around Us” Mean?

We see large numbers in many real-life situations.

For example:

population of a city;
number of people in a country;
money collected for a large project;
distance between planets;
number of books in a large library;
number of views on a popular video;
production of goods in a factory.

A number such as 75 is easy to imagine.

But numbers such as:

$75,00,00075,00,000$

$7,50,00,0007,50,00,000$

require a better understanding of place value.

This chapter helps students become comfortable with such numbers.

1. Understanding Place Value in Large Numbers

The value of a digit depends on its position in a number.

Consider:

$4,58,23,6174,58,23,617$

Using the Indian number system, we can separate it as:

4 crore
58 lakh
23 thousand
617

Therefore:

$4,58,23,6174,58,23,617$

is read as:

Four crore fifty-eight lakh twenty-three thousand six hundred seventeen.

The important point is that commas help us recognise groups of digits, but the actual value comes from place value.

Indian Place Value System

In the Indian system, commas are generally placed after the first three digits from the right and then after every two digits.

For example:

$123456789123456789$

is written as:

$12,34,56,78912,34,56,789$

The groups are:

Group	Value
Crore	12
Lakh	34
Thousand	56
Ones group	789

So the number is:

12 crore 34 lakh 56 thousand 789.

Important Indian Number Names

Number	Name
1,000	One thousand
10,000	Ten thousand
1,00,000	One lakh
10,00,000	Ten lakh
1,00,00,000	One crore
10,00,00,000	Ten crore
1,00,00,00,000	One arab

Students should pay particular attention to the difference between lakh and crore.

2. Reading Large Numbers

Let us consider:

$6,42,15,3086,42,15,308$

Separate the number according to the Indian system:

6 crore
42 lakh
15 thousand
308

Therefore, it is read as:

Six crore forty-two lakh fifteen thousand three hundred eight.

A useful method

When reading a large number:

Start from the left.
Identify the crore group.
Identify the lakh group.
Identify the thousand group.
Read the last three digits normally.

This method reduces mistakes.

3. Writing Numbers in the Indian System

Suppose the number is:

Seven crore twelve lakh five thousand forty-six.

Break it into groups:

Seven crore = 7,00,00,000
Twelve lakh = 12,00,000
Five thousand = 5,000
Forty-six = 46

Therefore:

$7,00,00,000+12,00,000+5,000+467,00,00,000+12,00,000+5,000+46$ $=7,12,05,046=7,12,05,046$

Final Answer

$7,12,05,046\boxed{7,12,05,046}$

Notice the zeroes in the thousands and hundreds places. They cannot simply be omitted.

4. Indian and International Number Systems

Large numbers are not grouped in exactly the same way in all countries.

The Indian system commonly uses:

thousand;
lakh;
crore.

The International system commonly uses:

thousand;
million;
billion;
trillion.

Example

Consider:

$10,00,00010,00,000$

In the Indian system, this is:

Ten lakh.

In the International system, the same number is:

One million.

Thus:

$10 lakh=1 million10\text{ lakh}=1\text{ million}$

Similarly:

$1 crore=10 million1\text{ crore}=10\text{ million}$

because:

$1,00,00,000=10,000,0001,00,00,000=10,000,000$

Indian and International Systems at a Glance

Indian System	International System
1 thousand	1 thousand
1 lakh	100 thousand
10 lakh	1 million
1 crore	10 million
10 crore	100 million
100 crore	1 billion

These relationships are useful when interpreting information presented using different number systems.

5. Comparing Large Numbers

To compare two large numbers, we should not start by comparing random digits.

A simple method is:

Step 1: Count the number of digits.

A number with more digits is larger.

For example:

$8,75,0008,75,000$

has six digits, while:

$75,00075,000$

has five digits.

Therefore:

$8,75,000>75,0008,75,000>75,000$

Step 2: If the number of digits is the same, compare from the left.

Consider:

$6,45,0006,45,000$

and

$6,35,0006,35,000$

Both contain six digits.

Compare the first digits:

$6=66=6$

Then compare the next digits:

$4>34>3$

Therefore:

$6,45,000>6,35,0006,45,000>6,35,000$

6. Exact and Approximate Values

An exact value is the actual value.

An approximate value is a value that is close to the actual value and is easier to use.

For example, suppose a stadium has exactly:

$48,76348,763$

seats.

The exact number is:

$48,76348,763$

But for a quick estimate, we might say:

$about 49,000\text{about }49,000$

The second number is an approximation.

When is approximation useful?

Approximation is helpful when:

an exact answer is not necessary;
we need to make a quick calculation;
we want to check whether an answer is reasonable;
we are dealing with very large quantities.

7. Rounding Off Numbers

Rounding means replacing a number with a nearby simpler number.

For example:

$48,76348,763$

rounded to the nearest thousand is:

$49,00049,000$

Why?

Look at the hundreds digit.

In 48,763, the hundreds digit is 7.

Since 7 is 5 or greater, we increase the thousands digit by 1.

Thus:

$48,763≈49,00048,763\approx49,000$

Rounding Rule

When rounding to a particular place:

Identify the digit you want to round.
Look at the digit immediately to its right.
If that digit is 0–4, keep the rounding digit unchanged.
If that digit is 5–9, increase the rounding digit by 1.
Replace the following digits with zeroes where necessary.

Example

Round:

$6,43,7826,43,782$

to the nearest thousand.

The thousands digit is 3.

The hundreds digit is 7.

Since:

$7≥57\ge5$

increase 3 to 4.

Therefore:

$6,43,782≈6,44,0006,43,782\approx6,44,000$

Final Answer

$6,44,000\boxed{6,44,000}$

8. Rounding to the Nearest Lakh

Consider:

$8,47,3218,47,321$

We want the nearest lakh.

The lakh digit is 4.

The next digit, the ten-thousands digit, is 4.

Since 4 is less than 5, the lakh digit remains unchanged.

Therefore:

$8,47,321≈8,00,0008,47,321\approx8,00,000$

Final Answer

$8,00,000\boxed{8,00,000}$

Another Example

Round:

$8,67,3218,67,321$

to the nearest lakh.

The lakh digit is 6.

The next digit is 6.

Since 6 is greater than 5, increase 6 to 7.

Therefore:

$8,67,321≈9,00,0008,67,321\approx9,00,000$

Final Answer

$9,00,000\boxed{9,00,000}$

9. Estimation

Estimation means finding a value that is close enough to the actual answer to make calculation easier.

Suppose we need to estimate:

$4,89,237+3,72,5144,89,237+3,72,514$

We can round both numbers to the nearest lakh.

$4,89,237≈5,00,0004,89,237\approx5,00,000$

and

$3,72,514≈4,00,0003,72,514\approx4,00,000$

Therefore:

$5,00,000+4,00,0005,00,000+4,00,000$ $=9,00,000=9,00,000$

So the estimated sum is:

$9,00,000\boxed{9,00,000}$

The exact sum may be different, but the estimate gives us a quick idea of the size of the answer.

Why Estimation Is Useful

Suppose you calculate an answer and obtain:

$90,00,00090,00,000$

while a quick estimate suggests that the result should be around:

$9,00,0009,00,000$

There is probably a calculation error.

Therefore, estimation can also be used as a checking tool.

10. Nearest Neighbours

A number can be understood by identifying nearby numbers.

For example, consider:

$5,00,0005,00,000$

Numbers around it might include:

$4,00,000,5,00,000,6,00,0004,00,000,\quad 5,00,000,\quad 6,00,000$

If a number is:

$5,42,0005,42,000$

it is closer to:

$5,00,0005,00,000$

than to:

$6,00,000.6,00,000.$

Thinking about nearby values helps students understand estimation and rounding instead of treating rounding as a rule to memorise blindly.

11. Patterns in Products

Large-number calculations can sometimes become easier when we notice patterns.

For example:

$25×4=10025\times4=100$

Therefore:

$250×4=1000250\times4=1000$

and:

$2500×4=100002500\times4=10000$

The pattern is created by the extra zeroes.

Similarly:

$125×8=1000125\times8=1000$

so:

$1,250×8=10,0001,250\times8=10,000$

and:

$12,500×8=1,00,00012,500\times8=1,00,000$

Recognising such patterns can make calculations faster and help students understand multiplication rather than relying only on long written calculations.

Examples

Example 1: Write a Number in Words

Write:

$5,24,07,3155,24,07,315$

in words using the Indian system.

Solution

Separate the number:

5 crore
24 lakh
7 thousand
315

Therefore:

Five crore twenty-four lakh seven thousand three hundred fifteen.

Final Answer

$Five crore twenty-four lakh seven thousand three hundred fifteen\boxed{\text{Five crore twenty-four lakh seven thousand three hundred fifteen}}$

Example 2: Write Words as a Number

Write three crore forty-five lakh six thousand twenty in figures.

Solution

Three crore:

$3,00,00,0003,00,00,000$

Forty-five lakh:

$45,00,00045,00,000$

Six thousand:

$6,0006,000$

Twenty:

$2020$

Combining them:

$3,45,06,0203,45,06,020$

Final Answer

$3,45,06,020\boxed{3,45,06,020}$

Example 3: Compare Two Numbers

Which is greater?

$7,45,23,1007,45,23,100$

$7,54,12,9007,54,12,900$

Solution

Both numbers have the same number of digits.

Compare from the left:

crore digits: 7 and 7 — equal;
next digits: 4 and 5.

Since:

$5>45>4$

we get:

$7,54,12,900>7,45,23,1007,54,12,900>7,45,23,100$

Final Answer

$7,54,12,900\boxed{7,54,12,900}$

is greater.

Example 4: Round to the Nearest Thousand

Round:

$3,68,4523,68,452$

to the nearest thousand.

Solution

The thousands digit is 8.

The hundreds digit is 4.

Since 4 is less than 5, the thousands digit remains 8.

Therefore:

$3,68,452≈3,68,0003,68,452\approx3,68,000$

Final Answer

$3,68,000\boxed{3,68,000}$

Example 5: Round to the Nearest Lakh

Round:

$7,63,4507,63,450$

to the nearest lakh.

Solution

The lakh digit is 7.

The ten-thousands digit is 6.

Since:

$6>56>5$

increase 7 to 8.

Therefore:

$7,63,450≈8,00,0007,63,450\approx8,00,000$

Final Answer

$8,00,000\boxed{8,00,000}$

Example 6: Estimate a Sum

Estimate:

$6,24,700+2,81,4006,24,700+2,81,400$

to the nearest lakh.

Solution

Round each number:

$6,24,700≈6,00,0006,24,700\approx6,00,000$ $2,81,400≈3,00,0002,81,400\approx3,00,000$

Now add:

$6,00,000+3,00,000=9,00,0006,00,000+3,00,000=9,00,000$

Final Answer

$9,00,000\boxed{9,00,000}$

Common Mistakes in Chapter 1

Mistake 1: Incorrect Commas

Students sometimes write:

$4,56,7894,56,789$

as:

$45,678945,6789$

This is incorrect in the Indian system.

The correct form is:

$4,56,7894,56,789$

Mistake 2: Confusing Lakh and Million

Remember:

$10 lakh=1 million10\text{ lakh}=1\text{ million}$

Therefore:

$1 lakh=0.1 million1\text{ lakh}=0.1\text{ million}$

Mistake 3: Rounding Without Looking at the Next Digit

Do not decide whether to round up merely by looking at the digit you are rounding.

Always check the digit immediately to its right.

Mistake 4: Treating an Estimate as the Exact Answer

If a question asks for an estimate, an approximate answer is expected.

If it asks for the exact value, do not round unnecessarily.

Mistake 5: Ignoring Zeroes

For example:

Four crore five lakh six thousand two hundred

must include the zeroes required by place value:

$4,05,06,2004,05,06,200$

The zeroes are important because they preserve the correct positions.

How to Prepare Chapter 1 for an Examination

A student preparing this chapter should be able to:

read large numbers;
write numbers in words;
write number names in figures;
use the Indian number system;
understand the International system;
convert between commonly used large-number units;
compare large numbers;
identify exact and approximate values;
round numbers;
estimate calculations;
identify useful numerical patterns.

A good revision session should include both direct questions and questions that require reasoning.

Chapter 1 Important Concepts

1. Indian Number System

Uses units such as:

thousand → lakh → crore → arab

2. International Number System

Uses:

thousand → million → billion → trillion

3. Estimation

Finding a reasonably close value to make calculations easier.

4. Rounding

Replacing a number by a nearby simpler number.

5. Number Patterns

Using relationships between numbers to make calculations easier and discover mathematical rules.

Practice Question 1

A science exhibition receives 3,48,725 visitors during its first phase and 2,67,480 visitors during its second phase.

Find:

the exact total number of visitors;
the estimated total to the nearest lakh.

Concept

This question tests addition of large numbers and estimation.

Step-by-Step Solution

Step 1: Find the exact total

$3,48,725+2,67,4803,48,725+2,67,480$

Add:

$3,48,7253,48,725$ $+2,67,480+2,67,480$ $=6,16,205=6,16,205$

Therefore, the exact total is:

$6,16,205\boxed{6,16,205}$

Step 2: Estimate to the nearest lakh

Round:

$3,48,725≈3,00,0003,48,725\approx3,00,000$

because the ten-thousands digit is 4.

Round:

$2,67,480≈3,00,0002,67,480\approx3,00,000$

because the ten-thousands digit is 6.

Therefore:

$3,00,000+3,00,000=6,00,0003,00,000+3,00,000=6,00,000$

Final Answers

Exact total:

$6,16,205\boxed{6,16,205}$

Estimated total:

$6,00,000\boxed{6,00,000}$

Practice Question 2

A district has a population of 8,72,450 people.

Write the population in words using the Indian number system.
Round the population to the nearest lakh.
Round it to the nearest thousand.

Concept

This question tests number reading and rounding.

Step 1: Write the number in words

$8,72,4508,72,450$

is:

Eight lakh seventy-two thousand four hundred fifty.

Step 2: Round to the nearest lakh

The lakh digit is 8.

The ten-thousands digit is 7.

Since:

$7>57>5$

increase 8 to 9.

Therefore:

$8,72,450≈9,00,0008,72,450\approx9,00,000$

Step 3: Round to the nearest thousand

The thousands digit is 2.

The hundreds digit is 4.

Since 4 is less than 5, the thousands digit remains unchanged.

Therefore:

$8,72,450≈8,72,0008,72,450\approx8,72,000$

Final Answers

Number name: Eight lakh seventy-two thousand four hundred fifty.

Nearest lakh:

$9,00,000\boxed{9,00,000}$

Nearest thousand:

$8,72,000\boxed{8,72,000}$

Class 7 Maths Chapter 1 Revision Points

1 lakh = 1,00,000.
10 lakh = 1 million.
1 crore = 1,00,00,000.
1 crore = 10 million.
In the Indian system, commas follow the 3-2-2-2 pattern from the right.
In the International system, digits are generally grouped in threes.
A number with more digits is larger than a number with fewer digits.
If two numbers have the same number of digits, compare them from the left.
For rounding, inspect the digit immediately to the right of the place being rounded.
Digits 0–4 generally leave the rounding digit unchanged.
Digits 5–9 increase the rounding digit by one.
Estimation gives a convenient approximate value.
Use estimation to check whether an exact calculation is reasonable.
Do not confuse an approximate value with an exact value.
Look for patterns in products instead of performing every calculation from scratch.

Frequently Asked Questions

What is the name of Class 7 Maths Chapter 1?

The current NCERT Grade 7 Mathematics Chapter 1 is Large Numbers Around Us in Ganita Prakash Part I.

What is taught in Large Numbers Around Us?

The chapter introduces large quantities and develops understanding of lakhs, crores, millions and billions. It also deals with reading and writing large numbers, number systems, approximation, estimation and numerical patterns. NCERT describes the chapter as an introduction to lakhs and crores, and millions and billions through explorations and contexts.

What is 1 lakh in numbers?

$1,00,000\boxed{1,00,000}$

How many lakhs are there in 1 crore?

$100 lakh\boxed{100\text{ lakh}}$

because:

$100×1,00,000=1,00,00,000100\times1,00,000=1,00,00,000$

How many millions are equal to 1 crore?

$10 million\boxed{10\text{ million}}$

What is the difference between exact and approximate values?

An exact value represents the actual quantity, while an approximate value is a nearby value used when an exact number is unnecessary or when quick calculation is preferred.

Why is estimation important?

Estimation helps students calculate quickly and check whether an exact answer is reasonable.

How should I learn Class 7 Maths Chapter 1?

First understand place value and number systems. Then practise reading and writing large numbers, comparing them, rounding them and estimating calculations.

Should I memorise the solutions?

No. Use solutions to understand the method. After studying an example, close the solution and try a similar problem independently.

Related Resources

SyllabusStudy.in can build the following supporting resources around this chapter:

Class 7 Maths Chapter 1 Notes
Class 7 Maths Chapter 1 Important Questions
Class 7 Maths Chapter 1 MCQs
Class 7 Maths Chapter 1 Practice Questions
Class 7 Maths Chapter 1 Revision Notes
Class 7 Maths Chapter 1 Practice Test
Class 7 Maths Chapter 1 Exercise Solutions
Class 7 Maths Complete Solutions

Chapter 1 Study Strategy

A strong way to study this chapter is:

Understand place value

↓

Learn Indian and International number systems

↓

Practise reading and writing numbers

↓

Compare numbers

↓

Learn rounding

↓

Practise estimation

↓

Study number patterns

↓

Attempt textbook questions independently

↓

Check the solution

↓

Take a practice test

This approach is more effective than memorising a list of answers.

Conclusion

Class 7 Maths Chapter 1 – Large Numbers Around Us builds an important foundation for working with large quantities. Students learn to understand numbers beyond the familiar thousands, work with lakhs and crores, relate them to millions and billions, and use estimation and rounding in practical situations.

The most useful habit in this chapter is to understand why a number is written, compared or rounded in a particular way. Once place value becomes clear, large-number calculations become much easier.

For exam preparation, combine concept revision with independent practice. Do not rely only on solution reading: attempt questions yourself, check your mistakes and then solve similar problems again.

Source Note

The current textbook information in this article has been checked against the official NCERT Ganita Prakash, Textbook of Mathematics, Grade 7, Part I, Reprint 2026–27. NCERT identifies Chapter 1 as Large Numbers Around Us.

The article’s explanations and practice questions are independently written for SyllabusStudy.in and are not reproduced from the textbook.